Algorithm

We wish to estimate (nowcast) the total current size of the COVID-19 outbreak, i.e. the total number of non-isolated individuals currently infected with SARS-CoV2. We need to estimate this number from case reports (the number of newly confirmed cases on a given day).

Case reports do not reflect those who are symptomatic but not yet diagnosed, nor those with latent infections (those who cary the virus but are not yet symptomatic). In addition, a number of individuals may be infected but never develop sysmptoms. These asymptomatic individuals may still transmit the virus. We assume that cases are isolated from the community at the time the case is reported.

In order to estimate the outbreak size, we must first estimate the number of symptomatic and latent infections in the community, accounting for cases that would be missed because they would never show symptoms, then sum those.

Algorithm details:

From case reports (the number of newly confirmed cases), we use monte carlo simulation to construct a line list, i.e. a list of symptom onset times for each individual case. The average delay from symtpom onset to case notification for the US is 2.67 days1. Individual simulated symtom onset times are distributed randomly around 2.67 days before the reporting date (exponential distribution).

A second simulation produces exposure dates for each infected individual. The average incubation period for the US is 7.67 days2. Individual simulated exposure times are distributed randomly around 7.67 days before the symptom onset date (gamma distribution with shape parameter ~4.18).

Now we have a complete line list for each case, including exposure date, symptom onset date, and reporting date (which is also the isolation date).

From the line list, we sum the number of individuals with latent infections on each date to produce a curve of the numbr of latent cases in the community. We do the same to find the number of individuals symptomatic infections on each date. These curves represent only the Latent and Symptomatic cases that were eventually reported.

Based on testing of passengers on the Princes Cruises ship in Yokohama, Japan, Mizumoto et al. estimated that the proportion of cases that are asymptomatic is 34.6% (95% CrI: 29.4%–39.8%)3. We assume asymptomatic cases are never detected. To account for these, we multiply both the number of Symptomatic cases and the number of Latent cases by \(\frac{1}{34.6\%}\).

Since the symptom onsets occur on average 2.67 days before reporting, we are only sure to have a complete estimate for the number of symptomatic individuals at some time prior to 2.67 days befor the present. We therefore throughout our estimates for the last several days, and forecast the number of Symptomatic individuals from that day back to the present. This is the “nowcast” of symptomatic individuals. We do the same for the curve of Latent individuals, throwing out estimates much prior to 7.67 before our last trusted estimate for the number of symtpomatic. Forecasting the number of Latent from that point forward gives us a nowcast of latent infections.

The sum of the Latent and Symptomatic curves and/or their forecasted curves gives us the estimate of the total number of infected, into the present.

Data

US Case Reports by State

US data are maintained by CEID and available here.

Data are compiled from https://en.wikipedia.org/wiki/2020_coronavirus_pandemic_in_the_United_States, which is updated by anonymous contributors.

We aim to update our dataset daily.

USA

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

AK

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

AL

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

AR

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

AZ

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

CA

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

CO

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

CT

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

DC

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

DE

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

FL

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

GA

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

HI

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

IA

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

IL

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

IN

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

KS

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

KY

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

LA

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

MA

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

MD

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

ME

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

MI

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

MN

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

MO

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

MS

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

MT

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

NC

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

ND

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

NE

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

NH

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

NJ

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

NM

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

NV

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

NY

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

OH

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

OK

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

OR

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

PA

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

RI

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

SC

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

SD

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

TN

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

TX

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

UT

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

VA

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

VT

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

WA

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

WI

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals

WY

Nowcast (outbreak size) = E + I = the number of non-isolated infected individuals


  1. Analysis by the Center for the Ecology of Infectious Diseases of US data. See supplemental information.

  2. Analysis by the Center for the Ecology of Infectious Diseases of US data suggests a mean incubation period of 7.67 days. See supplemental information.

  3. Kenji Mizumoto, Katsushi Kagaya, Alexander Zarebski, Gerardo Chowell. Estimating the Asymptomatic Ratio of 2019 Novel Coronavirus onboard the Princess Cruises Ship, 2020. medRxiv preprint. https://doi.org/10.1101/2020.02.20.20025866